{"paper":{"title":"Helmholtz and dispersive equations with variable coefficients on exterior domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Federico Cacciafesta, Piero D'Ancona, Renato Luca'","submitted_at":"2014-03-20T20:37:31Z","abstract_excerpt":"We prove smoothing estimates in Morrey-Campanato spaces for a Helmholtz equation $$\n  -Lu+zu=f,\n  \\qquad\n  -Lu:=\\nabla^{b}(a(x)\\nabla^{b}u)-c(x)u,\n  \\qquad\n  \\nabla^{b}:=\\nabla+ib(x) $$ with fully variable coefficients, of limited regularity, defined on the exterior of a starshaped compact obstacle in $\\mathbb{R}^{n}$, $n\\ge3$, with Dirichlet boundary conditions. The principal part of the operator is a long range perturbation of a constant coefficient operator, while the lower order terms have an almost critical decay. We give explicit conditions on the size of the perturbation which prevent t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5288","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}